Harmonic

“ To a more or less clearly defined harmonic nucleus are added softer tones, clashing with it, and thus forming about it an aura or atmosphere elsewhere compared to the mist which softens the outlines of the landscape. ”

“ A harmonic form, like a metrical form, was always a cluster of tones that could be both associated and distinguished.
It was a long time before these two means of organizing sound were used in combination. Until the seventeenth century metrical form was chiefly used, quite naturally, to define the gesticulatory part of musical material, the product of active emotion, while harmonic form gave coherence to the vocal part, the product of contemplative or religious emotion. ”

“ The fact that a repetition of sensations is productive of pleasant effects is not restricted to the realm of the visible. To-day, both the musician and the physicist know that the harmonic or the melodic addition of one tone to another affects us agreeably only when the added tone reproduces a part of the sensation which the first one excited. When I add an octave to a fundamental tone, I hear in the octave a part of what was heard in the fundamental tone. ”

“ A succession of tones without harmonic regulation is not a perfect element in music; neither is a succession of tones which have harmonic regulation but are void of rhythm. The beauty and expressiveness, especially the emotionality, of a musical composition depend upon the harmonies which either accompany the melody in the form of chords (a group of melodic intervals sounded simultaneously) , or are latent in the melody itself (harmonic intervals sounded successively) . Melody is Harmony analyzed; Harmony is Melody synthetized. ”

“ He will not be content with a mere accompaniment to some leading part. The harmonizing of these several melodies, that they may at every instant make recognized and well-proportioned combinations called chords, constitutes the modern science of harmony. This science is based upon the comparatively recent discoveries that Nature herself supplies a full chord, or cortége of harmonic sounds, to attend every single note, and others also to attend a union of two notes, and so on. ”

“ Of the many possible modes only two are used in our present system of music, the major and the minor. There is only one form of the major mode, and it is the one most people recall when they think of the scale. There are three forms of the minor mode, but of these the harmonic is the most frequently used. ”

“ The modern Dominant Harmonic Cadence is the passage of the mass of the harmony of the Dominant into the mass of the Tonic, and defines the key absolutely by giving successively the harmonies which represent the compound tone of the two most important roots in the scale, the most important of all coming last. ”

“ To forget the principles underlying three centuries of harmonic practice and revert to the methods of the mediaeval church composers, required an extraordinary degree of imaginative intuition; purposely and consistently to employ those methods as a foundation upon which to erect an harmonic structure most richly and elastically contrived—to vitalize the antique modes with the accumulated product of modern divination and accomplishment—was little less than an inspiration. ”

“ In the domain of tone-sensations, the harmonic notes, as we know, at first evade our immediate perception, though the timbre they give to the sound is at once noticed by every one, except those portions of the German race whose vocalization is faulty. ”

“ It is only through such conflict that the profounder combinations and mysteries of music in which an independent necessity reposes, discovers their source and ground; and for the same reason it is only in such profounder harmonic progressions that the arresting moments of melody originate. A bold style of musical composition will consequently part company with a purely consonant progression. ”

“ In this process of complication lie the infinite harmonic possibilities of sound as well as of colour. There are no two notes in music which, though when struck together are jarring, cannot be drawn into a perfect chord by the introduction of certain other notes. ”

“ Now, the modern minor mode is too firmly rooted in its minor tonic chord for the 16th-century feeling of an oblique harmonic scheme to be of more than secondary importance, though that feeling survives, as the discussion of key-relationships will show us. ”

“ By a proper adjustment of the initial amplitude and phase of each of these modes of vibration, so that their resultant shall represent the initial state of the string, we obtain a new representation of the whole motion of the string, in which it is seen to be the resultant of a series of simple harmonic vibrations whose periods are the fundamental period and its submultiples. The determination of the amplitudes and phases of the several simple harmonic vibrations so as to satisfy the initial conditions is an example of harmonic analysis. ”

“ HARMONICS, tones of higher pitch which accompany every perfect musical sound in a regular series. As they ascend they diminish in intensity, and approximate in pitch. If the piano be opened and a note—say D in the bass—be struck smartly and kept down, on listening attentively a succession of faint sounds will be heard, apparently rising out of the principal sound and floating round it. These are the harmonics. They are really constituents of the main musical tone, and are produced by the concurrent vibration of the aliquot parts of the string. ”

“ If the higher harmonic over-tones grow stronger, and even overpower the fundamental tone, the sound grows shriller, but when the discordant over-tones lying close together, higher than the tones just named, overpower the fundamental tone, the timbre becomes sharp and disagreeable. ”

“ Surely, it would be wiser to limit ourselves in our accompaniments to those harmonies which are as independent of “period” as the tunes themselves, for example, those of the diatonic genus, which have formed the basis and been the mainstay of harmonic music throughout its history, and upon which musicians of every age and of every school have, in greater or less degree, depended; and further, seeing that the genuine folk-air never modulates, never wavers from its allegiance to one fixed tonal centre, to avoid modulation, or use it very sparingly. ”

“ Every transition from one order of harmonic writing to another, from four-part harmony to three, or from five-part harmony to unison etc., must coincide with the introduction of a new idea, a fresh theme or phrase ”

“ We are used to thinking of chords thus welded by a common tone, and we demand this sort of coherence in our harmonic progressions, just as we demand that a horse's body shall be furnished with a horse's legs, or that a transitive verb shall have an object. ”

“ A knowledge of the principal chords, and familiarity with their manner of employment in composition, greatly facilitates the task, because the harmonic design furnishes in many cases the only unmistakable clue to the extremities of the melodic members. The difficulty finally vanishes only when the student has learned to appreciate the declamatory quality of all good melody, and can detect its inflections, its pauses ”

“ For their art was essentially contrapuntal—the combination of several parts each of equal importance with the rest, each in a sense pursuing its own course. In modern music the essential principle is harmonic: the chords formed by the combination of parts are derived and developed in reference to roots and keys. ”

“ Har′monist, one skilled in harmony: a musical composer.—Harmonic engine, an invention of Edison's, in which the energy of an electric current is used, by means of two small electro-magnets, to keep up the vibrations of a large and heavily-weighted tuning-fork whose arms are connected with two pistons working a miniature pump; Harmonic progression, a series of numbers the reciprocals of which are in arithmetical progression; Harmonic proportion, the relation of three quantities in harmonic progression—the 2d a harmonic mean between the 1st and 3d, as in the three numbers 2, 3, and 6 ”

“ An important auxiliary for the interpretation of the visibility curves is the harmonic analyzer—an instrument which sums up any number of simple harmonic motions, and which also analyzes any complex motion into its simple harmonic elements. ”

“ For example, if the compound sound is formed of six harmonics, the removal of the source of the sonorous vibrations, from the membrane to a distance equal to 14 of a wave-length of the 1st harmonic, will remove the 2d, 3d, 4th, 5th, and 6th harmonics to distances from the membrane equal respectively to 12, 34, 1, 114, and 112 wave-lengths. ”

“ The harmonic treatment, and more especially the enharmonic changes, are of extraordinary beauty and depth, and occasion remarkable effects of suspense and climax. Most admirable is the art with which the character of the movement as an introduction is maintained, and the defiant style of the following fugue clearly indicated, at the same time that the mind is tuned to a pitch of longing and melancholy which makes the entry of the categorical fugue a positive relief and stimulant. ”

“ The existence of the harmonic sense in rude natures, where music has not been heard, seems very difficult to account for, since, while it is true that any resonant tone contains the partial tones constituting the common chord, a resonant tone is very seldom heard among rude surroundings ”

“ So that I think the harmonica comes the nearest, as regards its tone, to that perfection, which is to be measured by its influence on our minds. And it is fortunate that this instrument (which chances to be the very one which imitates those nature-tones with such exactitude) happens to be just the very one which is incapable of lending itself to frivolity or ostentation, but exhibits its characteristic qualities in the purest of simplicity. ”

“ At other points the character and drift of the harmony is determined by quite a different principle—namely, that, the scale being conceived as indefinitely extended, the voices are agreed in selecting a particular section of it, the position of which determines not only the melodic character of each part but also the harmonic character of the whole, according to its greater or less remoteness from the scale in which major cardinal chords occupy a central position. ”

“ HARMONIC. In acoustics, a harmonic is a secondary tone which accompanies the fundamental or primary tone of a vibrating string, reed, &c.; the more important are the 3rd, 5th, 7th, and octave (see Sound; Harmony) . A harmonic proportion in arithmetic and algebra is such that the reciprocals of the proportionals are in arithmetical proportion; thus, if a, b, c be in harmonic proportion then 1/a, 1/b, 1/c are in arithmetical proportion; this leads to the relation 2/b=ac/ (a+c) . A harmonic progression or series consists of terms whose reciprocals form an arithmetical progression ”

“ Ah! could we but see the vibrations of the atmosphere which a single musical chord produces—the rolling bass, the gliding alto, the sweeping soprano, and the soaring tenor, rolling onward in one broad channel of harmony, with its myriad tributary streams of thirds and fifths, and its curling, twinkling, shifting, blending, soaring mists of delicate-toned harmonics, how would our enjoyment of music be enhanced! ”

“ CHAPTER XIII. The Scientific Basis of Harmonics—Some Peculiar Laws which Govern a Vibrating String—"Natural" and "Artificial" Harmonics—The Manner of Bowing Harmonics.
Harmonics.
In considering harmonics, the names of two of the greatest violin players the world has ever seen force themselves to one's mind:—Paganini and Spohr; the exponents of two schools of violin playing as diametrically opposed to each other as darkness is to light. ”

“ The relative importance of two harmonic disturbances depends upon their initial magnitudes, and upon the rate at which they grow. When the initial values are very small, the latter consideration is much the more important ”

“ It is often stated that the harmonics are obtained by increasing the tension of the lips and a crescendo by increasing the pressure of the breath.13 Victor Mahillon14 accounts for the harmonics by increased wind-pressure only. It is evident that the greater the tension of the lips, the greater the force of wind required to set them vibrating; therefore the force and velocity of the air must vary with the tension of the lips in order to produce a steady or musical sound. ”

“ Some, indeed, have been kind enough to attempt to give me a lucid explanation of what they are pleased to call a very simple natural phenomenon, and they prattle of enharmonics and sound vibrations, of nodes and super-tones, in a very impressive manner. ”

“ The harmonica, however much it excels all other instruments in the delicacy and duration of its tones, yet is confined to those of a soft and melancholy character and to slow, solemn movements, and can hardly be combined to advantage with other instruments. ”

“ In this truly scientific and ingenious work are to be found several discoveries in harmonics that have been enlarged upon by posterior writers on the subject. It contains four dissertations : the first treats of the similarity between the circular undulations occasioned in still water when a stone is thrown into it, and the propagation and motion of sound. ”

“ In the matter of harmony, for instance, there are certain types of procedure, certain progressions and sequences of chords, that are as stable and uniform as the types of animal or vegetable form. A horse, a dog, or a man is not a more definite organism than the two chords in the «Amen» of a hymn tune. This group or cluster of two chords, linked together by a common tone held over from one to the other, yet made distinct by progression of the other voices, is typical of a kind of harmonic form that long usage has established as part of our mental furniture. ”